Background
The authors note that conventional wisdom suggests that "human impacts to ecosystems are cumulative and lead only to long-term trajectories of environmental decline," and especially is this believed to be true in the case of coral reef ecosystems.

What was done
Using coral reefs and island societies as model social-ecological systems as per the work of Vitousek (2006) and Kirch (2007), Kittinger et al. say they "reconstructed human-environment relationships to test for sustainable levels of anthropogenic disturbance in human-dominated seascapes," with a reconstruction that "spans the past 700 years and is based on independent datasets on ecological conditions and social system change, which together provided the basis for reconstructing long-term social-ecological relationships in Hawaiian coral reef systems."

What was learned
The work of the nine researchers revealed "previously undetected recovery periods in Hawaiian coral reefs, including a historical recovery in the Main Hawaiian Islands (~AD 1400-1820) and an ongoing recovery in the Northwest Hawaiian Islands (~AD 1950-2009+)." And they report that "these recovery periods appear to be attributed to a complex set of changes in underlying social systems, which served to release reefs from direct anthropogenic stressor regimes," noting further that "recovery at the ecosystem level is associated with reductions in stressors over long time periods (decades+) and large spatial scales (>103 km2)."

What it means
Kittinger et al. state that their results "challenge conventional assumptions ... that human impacts to ecosystems are cumulative and lead only to long-term trajectories of environmental decline." In contrast, they write that "recovery periods reveal that human societies have interacted sustainably with coral reef environments over long time periods, and that degraded ecosystems may still retain the adaptive capacity and resilience to recover from human impacts."

References
Kirch, P.V. 2007. Hawaii as a model system for human ecodynamics. American Anthropologist109: 8-26.